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1997 Romania Team Selection Test
3
function f(x^2+y^2)=f(x^2-y^2)+f(2xy)
function f(x^2+y^2)=f(x^2-y^2)+f(2xy)
Source: Romanian TST 1997
June 18, 2011
function
algebra
Problem Statement
Find all functions
f
:
R
→
[
0
;
+
∞
)
f: \mathbb{R}\to [0;+\infty)
f
:
R
→
[
0
;
+
∞
)
such that:
f
(
x
2
+
y
2
)
=
f
(
x
2
−
y
2
)
+
f
(
2
x
y
)
f(x^2+y^2)=f(x^2-y^2)+f(2xy)
f
(
x
2
+
y
2
)
=
f
(
x
2
−
y
2
)
+
f
(
2
x
y
)
for all real numbers
x
x
x
and
y
y
y
.Laurentiu Panaitopol
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